Journal ArticleDOI
A minimax principle for nonlinear eigenvalue problems with applications to nonoverdamped systems
Reads0
Chats0
TLDR
In this paper, the theory of Rayleigh functionals for non-linear eigenvalue problems T(λ) u = 0 is extended to cases where the functional is defined only on a proper subset.Abstract:
The theory of Rayleigh functionals for non-linear eigenvalue problems T(λ) u = 0 is extended to cases where the functional is defined only on a proper subset. The theory applies to problems which do not satisfy an overdamping condition and yields a minimax characterization of eigenvalues. Applications to damped free vibrations of an elastic body are discussed.read more
Citations
More filters
Journal ArticleDOI
An integral method for solving nonlinear eigenvalue problems
TL;DR: In this paper, a numerical method for computing all eigenvalues (and the corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that lie within a given contour in the complex plane is proposed.
Journal ArticleDOI
Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods
Volker Mehrmann,Heinrich Voss +1 more
TL;DR: A new linearization technique is briefly introduced and demonstrated how it can be used to improve structure preservation and with this the accuracy and efficiency of linearization based methods.
Journal ArticleDOI
An Arnoldi method for nonlinear eigenvalue problems
TL;DR: In this paper, an iterative projection method for computing a few eigenvalues close to a given parameter is proposed, and the resulting projected eigenproblems of small dimension are solved by inverse iteration.
Journal ArticleDOI
The nonlinear eigenvalue problem
Stefan Güttel,Françoise Tisseur +1 more
TL;DR: This article surveys nonlinear eigenvalue problems associated with matrix-valued functions which depend nonlinearly on a single scalar parameter, with a particular emphasis on their mathematical properties and available numerical solution techniques.
Journal ArticleDOI
A Jacobi-Davidson-type projection method for nonlinear eigenvalue problems
Timo Betcke,Heinrich Voss +1 more
TL;DR: The subspace of approximants is constructed by a Jacobi-Davidson-type approach, and the arising eigenproblems of small dimension are solved by safeguarded iteration.
References
More filters
Book
Variational Methods for Eigenvalue Approximation
TL;DR: In this article, the authors provide a common setting for various methods of bounding the eigenvalues of a self-adjoint linear operator and emphasize their relationships, and provide a set of methods of quantifying the relationship between these eigenvectors.
Journal ArticleDOI
Some variational principles for a nonlinear eigenvalue problem
TL;DR: Shinbrot as discussed by the authors showed that the nonlinear eigenvalue problem has a sequence of eigenvalues converging to zero and a corresponding basis of eigvectors, with some conditions on L and M.